Example 3.2 cf. [1]} 
Let \(n=2\) , and \(P\subset \mathbb {R}^2\)  the trapezoid with the vertices \((0,0)\) , \((2,0)\) , \((0,1)\) , \((1,1)\) .
Take \(I=[(0,0),(0,1)]\) , and \(P^{\prime }=P\) .
Then \(Q=P+I\)  is analogous to a 5-gon obtained from \(\widehat{P}\)  by truncating the vertex \((3,0)\) .
Here \(\widehat{P}\)  is the trapezoid with the vertices \((0,0)\) , \((3,0)\) , \((0,2)\) , \((1,2)\) .
Then the push-pull polytope \(\Delta (P,Q)\subset \mathbb {R}^3\)  is the Minkowski sum of the FFLV polytope from Example REF  and the segment \(J=[(0,0,0),(1,0,0)]\) .
By shrinking \(J\)  we get a degeneration to the FFLV polytope.
The figure below shows \(P\) , \(Q\)  and \(\Delta (P,Q)\) , respectively (from left to right).
